The algebra teacher's guide to reteaching essential concepts and skills : 150 mini-lessons for correcting common mistakes

The Algebra Teacher’s Guide to Reteaching Essential Concepts and Skills......Page 1
About This Book......Page 5
About The Authors......Page 7
Acknowledgments......Page 9
Jossey-Bass Teacher......Page 10
Contents......Page 11
Section 1: Integers, Variables, and Expressions......Page 17
1.1: Using the Order of Operations......Page 18
1.2: Simplifying Expressions That Have Grouping Symbols......Page 20
1.3: Simplifying Expressions with Nested Grouping Symbols......Page 22
1.4: Using Positive Exponents and Bases Correctly......Page 24
1.5: Simplifying Expressions with Grouping Symbols and Exponents......Page 26
1.6: Evaluating Expressions......Page 28
1.7: Writing Expressions......Page 30
1.8: Writing Expressions Involving Grouping Symbols......Page 32
1.9: Identifying Patterns by Considering All of the Numbers......Page 34
1.10: Writing Prime Factorization......Page 36
1.11: Finding the Greatest Common Factor......Page 38
1.12: Finding the Least Common Multiple......Page 40
1.13: Classifying Counting Numbers, Whole Numbers, and Integers......Page 42
1.14: Finding Absolute Values and Opposites......Page 44
1.15: Adding Integers with Different Signs......Page 46
1.16: Subtracting Integers......Page 48
1.17: Multiplying Two Integers......Page 50
1.18: Multiplying More Than Two Integers......Page 52
1.19: Using Integers as Bases......Page 54
1.20: Dividing Integers......Page 56
1.21: Finding Absolute Values of Expressions......Page 58
1.22: Finding Square Roots of Square Numbers......Page 60
Section 2: Rational Numbers......Page 63
2.1: Classifying Counting Numbers, Whole Numbers, Integers, and Rational Numbers......Page 64
2.2: Simplifying Fractions......Page 66
2.3: Rewriting Mixed Numbers as Improper Fractions......Page 68
2.4: Comparing Rational Numbers......Page 70
2.5: Expressing Rational Numbers as Decimals......Page 72
2.6: Expressing Terminating Decimals as Fractions or Mixed Numbers......Page 74
2.7: Expressing Repeating Decimals as Fractions or Mixed Numbers......Page 76
2.8: Adding Rational Numbers......Page 78
2.9: Subtracting Rational Numbers......Page 80
2.10: Multiplying and Dividing Rational Numbers......Page 82
2.11: Expressing Large Numbers in Scientific Notation......Page 84
2.12: Evaluating Rational Expressions......Page 86
2.13: Writing Ratios Correctly......Page 88
2.14: Writing and Solving Proportions......Page 90
2.15: Expressing Fractions as Percents......Page 92
2.16: Expressing Percents as Fractions......Page 94
2.17: Solving Percent Problems......Page 96
2.18: Finding the Percent of Increase or Decrease......Page 98
2.19: Converting from One Unit of Measurement to Another Using theMultiplication Property of One......Page 100
Section 3: Equations and Inequalities......Page 103
3.1: Writing Equations......Page 104
3.2: Solving Equations by Adding or Subtracting......Page 106
3.3: Solving Equations by Multiplying or Dividing......Page 108
3.4: Solving Two-Step Equations with the Variable on One Side......Page 110
3.5: Solving Equations Using the Distributive Property.......Page 112
3.6: Solving Equations with Variables on Both Sides......Page 114
3.7: Solving Equations with Variables on Both Sides, Including Identities and Equations That Have No Solution......Page 116
3.8: Solving Absolute Value Equations......Page 118
3.9: Solving Absolute Value Equations That Have Two Solutions, One Solution, or No Solution......Page 120
3.10: Classifying Inequalities as True or False......Page 122
3.11: Writing Inequalities.......Page 124
3.12: Solving Inequalities with Variables on One Side......Page 126
3.13: Rewriting Combined Inequalities as One Inequality......Page 128
3.14: Solving Combined Inequalities—Conjunctions......Page 130
3.15: Solving Combined Inequalities—Disjunctions......Page 132
3.16: Solving Absolute Value Inequalities......Page 134
3.17: Solving Systems of Equations Using the Substitution Method......Page 136
3.18: Solving Systems of Equations Using the Addition-or-Subtraction Method......Page 138
3.19: Solving Systems of Equations Using Multiplication with the Addition-or-Subtraction Method......Page 140
3.20: Solving Systems of Equations Using a Variety of Methods......Page 142
3.21: Solving Systems of Equations That Have One Solution, No Solution, or an Infinite Number of Solutions......Page 144
3.22: Using Matrices—Addition, Subtraction, and Scalar Multiplication......Page 146
3.23: Identifying Conditions for Multiplying Two Matrices......Page 148
3.24: Multiplying Two Matrices......Page 150
Section 4: Graphs of Points and Lines......Page 153
4.1: Graphing on a Number Line......Page 154
4.2: Graphing Conjunctions......Page 156
4.3: Graphing Disjunctions......Page 158
4.4: Graphing Ordered Pairs on the Coordinate Plane......Page 160
4.5: Completing T-Tables......Page 162
4.6: Finding the Slope of a Line, Given Two Points on the Line......Page 164
4.7: Identifying the Slope and Y-Intercept from an Equation......Page 166
4.8: Using Equations to Find the Slopes of Lines......Page 168
4.9: Identifying Parallel and Perpendicular Lines, Given an Equation......Page 170
4.10: Using the X-Intercept and the Y-Intercept to Graph a Linear Equation......Page 172
4.11: Using Slope-Intercept Form to Graph the Equation of a Line......Page 174
4.12: Graphing Linear Inequalities in the Coordinate Plane......Page 176
4.13: Writing a Linear Equation, Given Two Points......Page 178
4.14: Finding the Equation of the Line of Best Fit......Page 180
4.15: Using the Midpoint Formula......Page 182
4.16: Using the Distance Formula to Find the Distance Between Two Points......Page 184
4.17: Graphing Systems of Linear Equations When Lines Intersect......Page 186
4.18: Graphing Systems of Linear Equations if Lines Intersect, Are Parallel, or Coincide......Page 188
Section 5: Monomials and Polynomials......Page 191
5.1: Applying Monomial Vocabulary Accurately......Page 192
5.2: Identifying Similar Terms......Page 194
5.3: Adding Polynomials......Page 196
5.4: Subtracting Polynomials......Page 198
5.5: Multiplying Monomials......Page 200
5.6: Using Powers of Monomials......Page 202
5.7: Multiplying a Polynomial by a Monomial......Page 204
5.8: Multiplying Two Binomials......Page 206
5.9: Multiplying Two Polynomials......Page 208
5.10: Dividing Monomials......Page 210
5.11: Dividing Polynomials......Page 212
5.12: Finding the Greatest Common Factor of Two or More Monomials......Page 214
5.13: Factoring Polynomials by Finding the Greatest Monomial Factor......Page 216
5.14: Factoring the Difference of Squares......Page 218
5.15: Factoring Trinomials if the Last TermIs Positive......Page 220
5.16: Factoring Trinomials if the Last TermIs Negative......Page 222
5.17: Factoring by Grouping......Page 224
5.18: Factoring Trinomials if the Leading Coefficient Is an Integer Greater Than 1......Page 226
5.19: Factoring the Sums and Differences of Cubes......Page 228
5.20: Solving Quadratic Equations by Factoring......Page 230
5.21: Solving Quadratic Equations by Finding Square Roots......Page 232
5.22: Solving Quadratic Equations Using the Quadratic Formula......Page 234
5.23: Using the Discriminant......Page 236
Section 6: Rational Expressions......Page 239
6.1: Using Zero and Negative Numbers as Exponents......Page 240
6.2: Using the Properties of Exponents That Apply to Division......Page 242
6.3: Using the Properties of Exponents That Apply to Multiplication and Division......Page 244
6.4: Identifying Restrictions on the Variable......Page 246
6.5: Simplifying Algebraic Fractions......Page 248
6.6: Adding and Subtracting Algebraic Fractions with Like Denominators......Page 250
6.7: Finding the Least Common Multiple of Polynomials......Page 252
6.8: Writing Equivalent Algebraic Fractions......Page 254
6.9: Adding and Subtracting Algebraic Fractions with Unlike Denominators......Page 256
6.10: Multiplying and Dividing Algebraic Fractions......Page 258
6.11: Solving Proportions......Page 260
6.12: Solving Equations That Have Fractional Coefficients......Page 262
6.13: Solving Fractional Equations......Page 264
Section 7: Irrational and Complex Numbers......Page 267
7.1: Simplifying Radicals......Page 268
7.2: Multiplying Radicals......Page 270
7.3: Rationalizing the Denominator......Page 272
7.4: Dividing Radicals......Page 274
7.5: Adding and Subtracting Radicals......Page 276
7.6: Multiplying Two Binomials Containing Radicals......Page 278
7.7: Using Conjugates to Simplify Radical Expressions......Page 280
7.8: Simplifying Square Roots of Negative Numbers......Page 282
7.9: Multiplying Imaginary Numbers......Page 284
7.10: Simplifying ComplexNumbers......Page 286
Section 8: Functions......Page 289
8.1: Determining if a Relation Is a Function......Page 290
8.2: Finding the Domain of a Function......Page 292
8.3: Finding the Range of a Function......Page 294
8.4: Using the Vertical Line Test......Page 296
8.5: Describing Reflections of the Graph of a Function......Page 298
8.6: Describing Vertical Shifts of the Graph of a Function......Page 300
8.7: Describing Horizontal and Vertical Shifts of the Graph of a Function......Page 302
8.8: Describing Dilations of the Graph of a Function......Page 304
8.9: Finding the Composite of Two Functions......Page 306
8.10: Finding the Inverse of a Function......Page 308
8.11: Evaluating the Greatest Integer Function......Page 310
8.12: Identifying Direct and Indirect Variation......Page 312
8.13: Describing the Graph of the Quadratic Function......Page 314
8.14: Using Rational Numbers as Exponents......Page 316
8.15: Using Irrational Numbers as Exponents......Page 318
8.16: Solving Exponential Equations......Page 320
8.17: Using the Compound Interest Formula......Page 322
8.18: Solving Radical Equations......Page 324
8.19: Writing Logarithmic Equations as Exponential Equations......Page 326
8.20: Solving Logarithmic Equations......Page 328
8.21: Using the Properties of Logarithms......Page 330
Common Core State Standards for Mathematics......Page 332